How do you solve using the completing the square method $x^2 - 6x - 16=0$ ?

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Answer 1 · 2016-03-22T17:40:01

The solutions are:
$x = 8$ and
$x = -2$

$x^2 - 6x - 16=0$

$x^2 - 6x = 16$

To write the Left Hand Side as a Perfect Square, we add 9 to both sides:

$x^2 - 6x + color(blue)(9)= 16+ color(blue)(9)$

$x^2 - 2*x*3 + 3^2 = 25$

Using the Identity $color(blue)((a-b)^2 = a^2 - 2ab + b^2$ , we get:

$(x-3)^2 = 25$

$x - 3 = sqrt 25$ or $x -3 = -sqrt25$

$x = 5 + 3 = 8$ or $x = -5 + 3 = -2$

The solutions are:
$x = 8$ and
$x = -2$

How do you solve using the completing the square method x^2 - 6x - 16=0x^2 - 6x - 16=0?